Preheat oven to 425°F. Toss together potato, onion, and 2 tablespoons oil on a rimmed baking sheet. Season with salt and pepper. Bake, stirring once, until potato and onion are tender, 24 to 26 minutes

Meanwhile, place kale and parsley in a food processor. Pulse until chopped, 4 to 5 times. Add Parmesan, garlic, lemon zest, and juice. Pulse, scraping down the sides as needed, until finely chopped, 10 to 12 times. With the machine running, slowly add remaining 1/3 cup oil through the feed tube. Season with salt and pepper.